Problem: Reduce to lowest terms: $- \dfrac{5}{6} \div \dfrac{6}{7} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{6}{7}$ is $ \dfrac{7}{6}$ Therefore: $ - \dfrac{5}{6} \div \dfrac{6}{7} = - \dfrac{5}{6} \times \dfrac{7}{6} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{7}{6}} = \dfrac{-5 \times 7}{6 \times 6} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{7}{6}} = \dfrac{-35}{36} $